Periodic solutions of a quasilinear wave equation

被引：2

作者：

Kondrat'ev, V. A. ^{[1
]}

Rudakov, I. A. ^{[2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

[2] Bryansk State Univ, Bryansk, Russia

来源：

MATHEMATICAL NOTES | 2009年 / 85卷 / 1-2期

关键词：

quasilinear wave equation; sine-Gordon equation; boundary condition of the third kind; Dirichlet boundary condition; Sturm-Liouville problem; Sobolev space; HOMOGENEOUS BOUNDARY-CONDITIONS; FORCED VIBRATIONS; COEFFICIENTS;

D O I：

10.1134/S0001434609010040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the properties of wave operators satisfying the periodicity condition with respect to time and homogeneous boundary conditions of the third kind and of Dirichlet type. We prove the existence of a nontrivial periodic (in time) sine-Gordon solution with homogeneous boundary conditions of the third kind and of Dirichlet type. We obtain theorems on the existence of periodic solutions of a quasilinear wave equation with variable (in x) coefficients and a boundary condition of the third kind.

引用

页码：34 / 50

页数：17

共 16 条

[1] Periodic solutions to nonlinear one dimensional wave equation with X-dependent coefficients [J].